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1.
It is well known that in the univariate case, up to an integer shift and possible sign change, there is no dyadic compactly
supported symmetric orthonormal scaling function except for the Haar function. In this paper we are concerned with the construction
of symmetric orthonormal scaling functions with dilation factor d=4. Several examples of such orthonormal scaling functions are provided in this paper. In particular, two examples of C
1 orthonormal scaling functions, which are symmetric about 0 and 1/6, respectively, are presented. We will then discuss how
to construct symmetric wavelets from these scaling functions. We explicitly construct the corresponding orthonormal symmetric
wavelets for all the examples given in this paper.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
2.
When approximation order is an odd positive integer a simple method is given to construct compactly supported orthogonal symmetric complex scaling function with dilation factor 3. Two corresponding orthogonal wavelets, one is symmetric and the other is antisymmetric about origin, are constructed explicitly. Additionally, when approximation order is an even integer 2, we also give a method to construct compactly supported orthogonal symmetric complex wavelets. In the end, there are several examples that illustrate the corresponding results. 相似文献
3.
Mauro Maggioni 《Applied and Computational Harmonic Analysis》2000,9(3):2032
For every integer M>2 we introduce a new family of biorthogonal MRAs with dilation factor M, generated by symmetric scaling functions with small support. This construction generalizes Burt–Adelson biorthogonal 2-band wavelets. For M{3,4} we are able to find simple explicit expressions for two different families of wavelets associated with these MRAs: one with better localization and the other with interesting symmetry–antisymmetry properties. We study the regularity of our scaling functions by determining their Sobolev exponent, for every value of the parameter and every M. We also study the critical exponent when M=3. 相似文献
4.
5.
通过方向多分辨分析把由一个函数生成的多频率小波推广到由有限个函数生成的多频率小波,给出由函数φ1,…,φn,…ψn(2^j1 ^j2-1)的平移生成Vj(1)空间的Riesz基的充分必要条件,同时给出该小波的分解式。 相似文献
6.
本文证明:如果来自多尺度分析(伸缩因子为矩阵)的小波是标准正交的,那么相对应的尺度函数也是标准正交的,其中函数f_s(x)∈L~2(R~n)(s=1,2,…,r,r是正整数)的标准正交性是指f_s(x)的整平移所构成的函数族为L~2(R~n)的标准正交系。结果表明,如果我们想从多尺度分析出发构造正交小波,那么该多尺度分析必须有正交尺度函数。 相似文献
7.
We investigate full rank interpolatory vector subdivision schemes whose masks are positive definite on the unit circle except
the point z=1. Such masks are known to give rise to convergent schemes with a cardinal limit function in the scalar case.
In the full rank vector case, we show that there also exists a cardinal refinable function based on this mask, however, with
respect to a different notion of refinability which nevertheless also leads to an iterative scheme for the computation of
vector fields. Moreover, we show the existence of orthogonal scaling functions for multichannel wavelets and give a constructive
method to obtain these scaling functions.
AMS subject classification (2000) 42C40, 65T60, 65D05 相似文献
8.
This paper is on the angle–frequency localization of periodic scaling functions and wavelets. It is shown that the uncertainty
products of uniformly local, uniformly regular and uniformly stable scaling functions and wavelets are uniformly bounded from
above by a constant. Results for the construction of such scaling functions and wavelets are also obtained. As an illustration,
scaling functions and wavelets associated with a family of generalized periodic splines are studied. This family is generated
by periodic weighted convolutions, and it includes the well‐known periodic B‐splines and trigonometric B‐splines.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
9.
向量值双正交小波的存在性及滤波器的构造 总被引:1,自引:0,他引:1
引进了向量值多分辨分析与向量值双正交小波的概念.讨论了向量值双正交小波的存在性.运用多分辨分析和矩阵理论,给出一类紧支撑向量值双正交小波滤波器的构造算法.最后,给出4-系数向量值双正交小波滤波器的的构造算例. 相似文献
10.
Multivariate Compactly Supported Fundamental Refinable Functions, Duals, and Biorthogonal Wavelets 总被引:8,自引:0,他引:8
In areas of geometric modeling and wavelets, one often needs to construct a compactly supported refinable function φ which has sufficient regularity and which is fundamental for interpolation [that means, φ(0)=1 and φ(α)=0 for all α∈ Z s ∖{0}].
Low regularity examples of such functions have been obtained numerically by several authors, and a more general numerical scheme was given in [1]. This article presents several schemes to construct compactly supported fundamental refinable functions, which have higher regularity, directly from a given, continuous, compactly supported, refinable fundamental function φ. Asymptotic regularity analyses of the functions generated by the constructions are given.The constructions provide the basis for multivariate interpolatory subdivision algorithms that generate highly smooth surfaces.
A very important consequence of the constructions is a natural formation of pairs of dual refinable functions, a necessary element in constructing biorthogonal wavelets. Combined with the biorthogonal wavelet construction algorithm for a pair of dual refinable functions given in [2], we are able to obtain symmetrical compactly supported multivariate biorthogonal wavelets which have arbitrarily high regularity. Several examples are computed. 相似文献
Low regularity examples of such functions have been obtained numerically by several authors, and a more general numerical scheme was given in [1]. This article presents several schemes to construct compactly supported fundamental refinable functions, which have higher regularity, directly from a given, continuous, compactly supported, refinable fundamental function φ. Asymptotic regularity analyses of the functions generated by the constructions are given.The constructions provide the basis for multivariate interpolatory subdivision algorithms that generate highly smooth surfaces.
A very important consequence of the constructions is a natural formation of pairs of dual refinable functions, a necessary element in constructing biorthogonal wavelets. Combined with the biorthogonal wavelet construction algorithm for a pair of dual refinable functions given in [2], we are able to obtain symmetrical compactly supported multivariate biorthogonal wavelets which have arbitrarily high regularity. Several examples are computed. 相似文献
11.
紧支撑正交对称和反对称小波的构造 总被引:10,自引:0,他引:10
1.引言 近年来,人们分别从数学和信号的观点对正交小波进行了广泛的研究.尤其是2尺度小波,它克服了短时 Fourier变换的一些缺陷.目前最常用的 2尺度小波是 Daubechies 小波,但 2尺度小波也存在一些问题:如 Daubechies[2]已证明了除 Haar小波外不存在既正交又对称的紧支撑 2尺度小波.因此人们提出了 a尺度小波理论[3]-[6],文献[4]-[6]对 4尺度小波迸行研究.本文的目的是研究4尺度因子时紧支撑正交对称和反对称小波的构造方法.并指出对同一紧支撑正交对称尺度函数而言,… 相似文献
12.
Kjetil Røysland 《Journal of Fourier Analysis and Applications》2008,14(2):267-285
We give an equivariant version of Packer and Rieffel’s theorem on sufficient conditions for the existence of orthonormal wavelets
in projective multiresolution analysis. Suppose that the scaling functions are invariant with respect to some finite group
action. We give sufficient conditions for the existence of wavelets with similar invariance.
Research supported in part by the Research Council of Norway, project number NFR 154077/420. Some of the final work was also
done with the support from the project NFR 170620/V30. 相似文献
13.
Generalized cardinal B-splines are defined as convolution products of characteristic functions of self-affine lattice tiles
with respect to a given integer scaling matrix. By construction, these generalized splines are refinable functions with respect
to the scaling matrix and therefore they can be used to define a multiresolution analysis and to construct a wavelet basis.
In this paper, we study the stability and linear independence properties of the integer translates of these generalized spline
functions. Moreover, we give a characterization of the scaling matrices to which the construction of the generalized spline
functions can be applied. 相似文献
14.
Divergence-free wavelets are successfully applied to numerical solutions of Navier-Stokes equation and to analysis of incompressible
flows. They closely depend on a pair of one-dimensional wavelets with some differential relations. In this paper, we point
out some restrictions of those wavelets and study scaling functions with the differential relation; Wavelets and their duals
are discussed; In addition to the differential relation, we are particularly interested in a class of examples with the interpolatory
property; It turns out there is a connection between our examples and Micchelli’s work. 相似文献
15.
周建锋 《数学的实践与认识》2014,(3)
研究由三元双正交插值尺度函数构造对应的双正交小波滤波器的矩阵扩充问题.当给定的一对三元双正交尺度函数中有一个为插值函数时,利用提升思想与矩阵多相分解方法,给出一类三元双正交小波滤波器的显示构造公式和一个计算实例.讨论了三元双正交小波包的的性质. 相似文献
16.
In this paper, a complete parameterization for the 3-band compact wavelet systems is presented. Using the parametric result,
a program of the filterbank design is completed, which can give not only the filterbanks but also the graphs of all possible
scaling functions and their corresponding wavelets. Especially some symmetric wavelets with small supports are given. Finally
an algebraic structure for this kind of wavelet systems is characterized. 相似文献
17.
Compactly supported (bi)orthogonal wavelets generated by interpolatory refinable functions 总被引:7,自引:0,他引:7
This paper provides several constructions of compactly supported wavelets generated by interpolatory refinable functions.
It was shown in [7] that there is no real compactly supported orthonormal symmetric dyadic refinable function, except the
trivial case; and also shown in [10,18] that there is no compactly supported interpolatory orthonormal dyadic refinable function.
Hence, for the dyadic dilation case, compactly supported wavelets generated by interpolatory refinable functions have to be
biorthogonal wavelets. The key step to construct the biorthogonal wavelets is to construct a compactly supported dual function
for a given interpolatory refinable function. We provide two explicit iterative constructions of such dual functions with
desired regularity. When the dilation factors are larger than 3, we provide several examples of compactly supported interpolatory
orthonormal symmetric refinable functions from a general method. This leads to several examples of orthogonal symmetric (anti‐symmetric)
wavelets generated by interpolatory refinable functions.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
18.
Mehrdad Lakestani Mahmood Jokar Mehdi Dehghan 《Mathematical Methods in the Applied Sciences》2011,34(11):1317-1329
The main aim of this paper is to apply the trigonometric wavelets for the solution of the Fredholm integro‐differential equations of nth‐order. The operational matrices of derivative for trigonometric scaling functions and wavelets are presented and are utilized to reduce the solution of the Fredholm integro‐differential equations to the solution of algebraic equations. Furthermore, we get an estimation of error bound for this method. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
19.
带小波函数的Cauchy主值积分的数值计算 总被引:4,自引:1,他引:3
1 引言 众所周知,小波方法在信号处理和图像处理方面发挥了举世瞩目的成就。近年来人们研究小波方法在数值分析方面的应用。期望在数值求解微分方程和积分方程方面发挥良好的作用。本文研究带有小波函数的Cauchy主值积分 的数值计算方法,其中Φ(x)是紧支撑的尺度函数。这是数值求解积分方程的核心问题之一。 1.l 多分辩分析 空间L~2(R)中的一个多分辩分析是这样的闭子空间列{V_j},它满足下列条件 1) 2) 3) 4)存在尺度函数,使构成V_o的Riesz基,从而也存在序列使满足双尺度方程 相似文献
20.
Xiaolin Zhou 《Numerical Methods for Partial Differential Equations》2004,20(2):193-198
This note presents a wavelets‐Galerkin scheme for the numerical solution of a Stokes problem by using the scaling function of a symmetric biorthogonal spline wavelets that can be modified to generate the divergence‐free wavelets. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 193–198, 2004 相似文献